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A time-invariant multi-frequency modeling technique is proposed for pulse-width-modulated (PWM) dc-dc converters. The proposed methodology distinguishes between different types of modulation carrier signals (e.g., sawtooth and isosceles triangle carriers). A straightforward systematic procedure is proposed to automatically convert the conventional state-space time-variant model to the proposed time-invariant model. Hence, high-order time-invariant models can be easily developed for system design and stability analysis purposes. Closed-loop time-domain and open-loop frequency-domain responses extracted from a laboratory-scale Cuk converter have verified the proposed methodology. [ABSTRACT FROM PUBLISHER]